Final answer:
Based on the standard deviation of the sample exceeding the maximum threshold, the cereal box filling machine likely needs recalibration. Statistical analysis plays a vital role in such decisions, as it helps in identifying significant deviations that can impact quality control in manufacturing processes.
Step-by-step explanation:
The question pertains to determining whether recalibration of machinery is necessary based on the standard deviation of weights of cereal boxes. In the given scenario, a plant manager has the standard deviation defined at a maximum threshold of 0.5 ounces. However, upon sampling and weighing 84 cereal boxes, the actual standard deviation was found to be 0.54 ounces. Therefore, this indicates that the machine likely requires recalibration, as the standard deviation exceeded the established threshold, reflecting inconsistency in the weights beyond the acceptable level.
Statistical analysis and understanding variations in data are crucial in making such decisions. The ability to collect, organize, and analyze data using statistics and spreadsheet programs allows researchers and managers to identify patterns, and deviations from those patterns, and determine whether these deviations are significant enough to warrant action.
This practical application of statistics is essential not only in manufacturing but in various fields, such as economics and social sciences, where comprehending and applying statistical methods form an integral part of the curriculum.